Which center bears the primary responsibility for generating the respiratory rhythm, but is influenced by several other centers

This is the Ventral Regulatory Group-VRG

Explanation:

In the medulla,there are four groups of neurons which forms the exhalation parts of the   respiratory  control.These 4 groups are called the VRG.They occupy 5mm anterior in length, and laterally positioned to the dorsal respiratory group.They are therefore said to occupy the ventrolateral part of the medulla.

The dorsal respiratory group(DRG) consists of the inspiration neurons,contrary to the VRG. They do not extend to the DRG,but the DRG, extends to them

They(VRG) function in propagating action potentials needed for the mechanisms of respiration.(exhalations), and Inspirations

your answer is "the 1950's"